Studies in Applied Mathematics最新文献

{"title":"Bright and Dark Breathers on an Elliptic Wave in the Defocusing mKdV Equation","authors":"Dmitry E. Pelinovsky,&nbsp;Rudi Weikard","doi":"10.1111/sapm.70170","DOIUrl":"https://doi.org/10.1111/sapm.70170","url":null,"abstract":"<p>Breathers on an elliptic wave background consist of nonlinear superpositions of a soliton and a periodic wave, both traveling with different wave speeds and interacting periodically in the space-time. For the defocusing modified Korteweg–de Vries equation, the construction of general breathers has been an open problem since the elliptic wave is related to the elliptic degeneration of the hyperelliptic solutions of genus two. We have found a new representation of eigenfunctions of the Lax operator associated with the elliptic wave, which enables us to solve this open problem and to construct two families of breathers with bright (elevation) and dark (depression) profiles.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70170","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146083353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Large-Amplitude Periodic Solutions to the Steady Euler Equations With Piecewise Constant Vorticity","authors":"Alex Doak,&nbsp;Karsten Matthies,&nbsp;Jonathan Sewell,&nbsp;Miles H. Wheeler","doi":"10.1111/sapm.70163","DOIUrl":"https://doi.org/10.1111/sapm.70163","url":null,"abstract":"<p>We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation theory, we rigorously construct curves of solutions that terminate either with stagnation on the interface or when the conformal equivalence between one of the layers and a strip breaks down in a <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$C^1$</annotation>\u0000 </semantics></math> sense. We give numerical evidence that, depending on parameters, these occur either as a corner forming on the interface or as one of the layers developing regions of arbitrarily thin width. Our proof relies on a novel formulation of the problem as an elliptic system for the velocity components in each layer, conformal mappings for each layer, and a horizontal distortion, which makes these mappings agree on the interface. This appears to be the first local formulation for a multi-layer problem, which allows for both overhanging wave profiles and stagnation points.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70163","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146096463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weak Shock Diffraction and Reflection in Extended Chaplygin Gas","authors":"Gaurav Upadhyay,&nbsp;Anuwedita Singh,&nbsp;L. P. Singh","doi":"10.1111/sapm.70178","DOIUrl":"https://doi.org/10.1111/sapm.70178","url":null,"abstract":"<div>\u0000 \u0000 <p>The study has analyzed the diffraction and reflection phenomena of a weak shock interacting with a right-angled wedge in the context of a more realistic extended Chaplygin gas. Asymptotic solutions to the two-dimensional Euler system have been derived under appropriate boundary conditions that characterize the diffraction of a weak shock from the wedge. In this study, the effects of the specific gas considered are carefully modeled, and their influence on the overall flow configuration is examined. In particular, a detailed investigation of the local structure near a singular point is conducted, highlighting the significant role of the considered gas behavior in shaping the flow dynamics.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146091433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Anomalous Scattering of Lumps and Interaction of Lump Chains in the Modified Kadomtsev–Petviashvili-I Equation","authors":"Tianwei Qiu,&nbsp;Zhen Wang,&nbsp;Xiangyu Yang","doi":"10.1111/sapm.70174","DOIUrl":"https://doi.org/10.1111/sapm.70174","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents a systematic study of lump solutions and lump chain solutions in the modified Kadomtsev–Petviashvili-I equation. Using the long-wave limit method, we derive both standard lump solutions and plane lump solutions from line-soliton solutions. Through detailed asymptotic analysis, it is shown that standard lump solutions exhibit normal scattering. We further investigate lump chain solutions and identify elastic interactions with explicit phase shifts, as well as distinctive resonant patterns, including a characteristic “Y”-shaped resonance and a unique parallel resonance phenomenon. An improved long - wave limit approach is introduced to construct higher-order lump solutions from lump chain solutions, yielding second-order lump solutions, second-order lump chain solutions, and semi-rational soliton solutions. Notably, the second-order lump solutions exhibit anomalous scattering, in which individual lumps propagate along curved trajectories despite sharing the same asymptotic velocity. Our analysis also establishes a connection between lump solutions and the root structure of Yablonskii–Vorob'ev polynomials. These results deepen the understanding of nonlinear wave interactions in (2 + 1)-dimensional integrable systems.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146002126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniform Dynamical Stability of Pullback Attractors for Lagrangian-Averaged Navier–Stokes Equations With Delays","authors":"Shuang Yang,&nbsp;Romulo D. Carlos,&nbsp;Qiangheng Zhang","doi":"10.1111/sapm.70175","DOIUrl":"https://doi.org/10.1111/sapm.70175","url":null,"abstract":"<div>\u0000 \u0000 <p>The paper is devoted to the dynamical stability of pullback attractors for non-autonomous Lagrangian-averaged Navier–Stokes equations with delays. First, using the Ascoli–Arzelà theorem, we prove the pullback asymptotic compactness of solution operators to establish the existence of pullback attractors. Second, we prove the pointwise upper semicontinuity of pullback attractors as the delay time approaches zero. Eventually, we further investigate their uniform upper semicontinuity when the delay time converges to zero. Combining these two results, the latter strengthens the former. To the best of our knowledge, this paper appears to be the first to address both types of upper semicontinuity for pullback attractors, particularly the interesting uniform case.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146002127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Energy Balance and Optical Theorem for Time-Modulated Subwavelength Resonator Arrays","authors":"Erik Orvehed Hiltunen,&nbsp;Liora Rueff","doi":"10.1111/sapm.70168","DOIUrl":"https://doi.org/10.1111/sapm.70168","url":null,"abstract":"<div>\u0000 \u0000 <p>We study wave propagation through a one-dimensional array of subwavelength resonators with periodically time-modulated material parameters. Focusing on a high-contrast regime, we use a scattering framework based on Fourier expansions and scattering matrix techniques to capture the interactions between an incident wave and the temporally varying system. This way, we derive a formulation of the total energy flux corresponding to time-dependent systems of resonators. We show that the total energy flux is composed of the transmitted and reflected energy fluxes and derive an optical theorem which characterizes the energy balance of the system. We provide a number of numerical experiments to investigate the impact of the time-dependency, the operating frequency, and the number of resonators on the maximal attainable energy gain and energy loss. Moreover, we show the existence of lasing points, at which the total energy diverges. Our results lay the foundation for the design of energy dissipative or energy amplifying systems.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145983532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Degenerate Third Painlevé Equation: Complete Asymptotic Classification of Solutions in the Neighborhood of the Regular Singular Point","authors":"A. V. Kitaev,&nbsp;A. Vartanian","doi":"10.1111/sapm.70146","DOIUrl":"https://doi.org/10.1111/sapm.70146","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;We give a classification for the small-&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;annotation&gt;$tau$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; asymptotic behaviors of solutions to the degenerate third Painlevé equation, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;8&lt;/mn&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;ab&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;msup&gt;\u0000 &lt;","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145904880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Formation of Vacuum State and Delta Shock in the Solution of Two-Dimensional Riemann Problem for Zero Pressure Gas Dynamics","authors":"Anamika Pandey,&nbsp;T. Raja Sekhar","doi":"10.1111/sapm.70169","DOIUrl":"https://doi.org/10.1111/sapm.70169","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we investigate the two-dimensional pressureless Euler equations with three constant Riemann initial data. Our primary focus is on the wave interactions involving contact discontinuities and delta shocks. A distinguishing feature of the solution is the emergence of a delta shock wave which is characterized by a Dirac delta function appearing in both the density and internal energy variables. By exploiting generalized characteristic analysis, nine topologically distinct solution patterns are derived. Some of these configurations exhibit features similar to Mach-reflection and in certain cases, vacuum regions may also develop. To validate the theoretical results, numerical simulations are carried out using a semidiscrete central upwind scheme. The comparison between analytical and numerical results demonstrates excellent agreement, providing deeper insights into the complex dynamics of wave interactions in the pressureless Euler system.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145905032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Propagation Dynamics for a Spatial Discrete Waterborne Pathogen Model With Temporal Periodicity","authors":"Jinling Zhou,&nbsp;Yu Yang,&nbsp;Cheng-Hsiung Hsu","doi":"10.1111/sapm.70167","DOIUrl":"https://doi.org/10.1111/sapm.70167","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper is concerned with the propagation dynamics for a spatial discrete waterborne pathogen model with temporal periodicity. We firstly establish the spreading speed of the model. Then, applying the asymptotic fixed-point theorem via a pair of time-periodic upper and lower solutions, we show that the model admits time-periodic traveling waves when the basic reproduction number is larger than one and the wave speed is greater than a threshold speed. In addition, when the basic reproduction number is either smaller than one; or larger than one but the wave speeds are less than the threshold speed, we further prove the non-existence of time-periodic traveling waves by using the methods of comparison principle. From our result, one can see the minimum wave speed for the time-periodic traveling waves is exactly the same with the spreading speed of the model.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145905034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Surface Wave Solutions in 1D and 2D for the Broer–Kaup–Boussinesq–Kupershmidt System","authors":"Darryl D. Holm,&nbsp;Ruiao Hu,&nbsp;Hanchun Wang","doi":"10.1111/sapm.70165","DOIUrl":"https://doi.org/10.1111/sapm.70165","url":null,"abstract":"<p>The Broer–Kaup–Boussinesq–Kupershmidt (BKBK) system is a singular perturbation of the classical shallow water equations which modifies their transport velocity to depend on wave elevation slope. This modification introduces backward diffusion terms proportional to a real parameter <span></span><math>\u0000 <semantics>\u0000 <mi>κ</mi>\u0000 <annotation>$kappa$</annotation>\u0000 </semantics></math>. These terms also make the BKBK system completely integrable as a Hamiltonian system. Remarkably, when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>κ</mi>\u0000 <mo>=</mo>\u0000 <mi>i</mi>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$kappa =i/2$</annotation>\u0000 </semantics></math>, the BKBK system may be transformed into the focusing nonlinear Schrödinger equation. Thus, the BKBK system with its real parameter <span></span><math>\u0000 <semantics>\u0000 <mi>κ</mi>\u0000 <annotation>$kappa$</annotation>\u0000 </semantics></math> is complementary to the traditional modulational approach for water waves. We investigate the Lie algebraic and variational properties of the BKBK system in this paper, and we study its solution behavior in certain computational simulations of regularized versions of the 1D and 2D BKBK systems.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70165","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145904874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}